Multi-parameter Estimation Method for Partially Polarized Signals Based on Non-Coincident and Non-Uniform Polarization Arrays

Abstract

The present invention discloses a multi-parameter estimation method for partially polarized signals based on a non-coplanar non-uniform polarization array. The implementation steps of the method of the present invention are as follows: arranging a non-coplanar non-uniform polarization array; constructing a receiving model for partially polarized signals and sampling; obtaining the array sample covariance matrix and its error statistical distribution; constructing and solving an optimization problem for reconstructing the theoretical covariance matrix of a coplanar uniform polarization array; estimating the signal arrival direction based on the reconstructed theoretical covariance matrix of the coplanar uniform polarization array; solving the signal coherence matrix and estimating the signal polarization parameters. The array of the method of the present invention adopts a non-coplanar manner, and the phase centers of each polarization unit do not overlap. On the one hand, the mutual coupling problem existing between the polarization units of the coplanar array is avoided; on the other hand, each array element has only one RF channel, saving resources. Then, the array adopts a non-uniform manner, lifting the limitation of the uniform array on the array aperture and ensuring no ambiguity in the arrival direction estimation.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and particularly relates to the multi-parameter estimation of partially polarized signals. Specifically, it is a multi-parameter estimation method for partially polarized signals based on a non-collocated non-uniform polarization array. Background Technique

[0002] Array antenna technology is used to estimate parameters such as the direction of arrival of signals and is widely applied in technical fields such as radar and communication. Previous studies mostly assumed that the array is a scalar array, that is, the polarization of the array is single. In this case, when the signal polarization is different from the array polarization, it will lead to polarization mismatch and reduce the signal-to-noise ratio. To solve this problem, a polarization array (fully called a polarization-sensitive array) was proposed. The polarization array contains elements with different polarizations and can receive different polarization components of signals. In addition to solving the polarization mismatch problem, the polarization array also makes it possible to estimate the signal polarization parameters. Based on the polarization array, researchers have conducted a large number of studies on fully polarized signals. The polarization parameters of fully polarized signals are fixed, but in some applications, the polarization of the signal changes with time. Such signals are called partially polarized signals. Fully polarized signals are a special case of partially polarized signals, so the research on partially polarized signals is more general.

[0003] For the convenience of signal processing, each element in a polarization array is usually composed of multiple different polarization units with overlapping phase centers, and each element has the same structure, such as the method adopted in Reference 1 (Shu T, Wang K, He J, et al. Subspace-Based Method for Direction Finding of Multiple Partially Polarized Signals [J]. Chinese Journal of Electronics, 2018, 27(1): 206-212). The overlapping of the phase centers of multiple polarization units is called co-location. The co-location of polarization units brings two problems. On the one hand, since each polarization unit needs to be equipped with a radio frequency channel, one element corresponds to multiple radio frequency channels, which will increase the hardware cost. On the other hand, the co-located polarization units will cause mutual coupling between the units, reducing the parameter estimation performance. To address this problem, Reference 2 (F. Liu, H. Li, W. Xia and Y. Wang, A DOA and Polarization Estimation Method Using a Spatially Non-Collocated Vector Sensor Array, 2014 IEEE China Summit & International Conference on Signal and Information Processing (ChinaSIP), 2014, pp. 763-767) proposed a non-co-located array, in which the phase centers of each polarization unit do not overlap and each forms an element independently. However, due to its uniform structure, in order to avoid the ambiguity of the incident wave direction, the spacing between different polarization units needs to be no more than one-quarter of the wavelength, which will reduce the array aperture and increase the mutual coupling. In addition, the parameter estimation method proposed in this reference is for the case where the signal is completely polarized and is not applicable to partially polarized signals. Summary of the Invention

[0004] An object of the present invention is to propose a multi-parameter estimation method for partially polarized signals based on a non-co-located non-uniform polarization array in view of the deficiencies of the prior art.

[0005] The present invention is implemented through the following technical solutions:

[0006] Step (1) Arrange a non-co-located non-uniform polarization array:

[0007] The non-co-located non-uniform polarization array is composed of two non-uniform sub-arrays. The polarizations of the two sub-arrays are orthogonal to each other and jointly form a uniform linear array. Each element in the sub-array is composed of only one polarization unit, that is, each element has only one output port.

[0008] The uniform linear array arrangement is specifically as follows: In a three-dimensional rectangular coordinate system, two non-uniform sub-arrays are placed along the y-axis, namely the x-direction polarized sub-array and the y-direction polarized sub-array; where:

[0009] The x-direction polarized sub-array contains M1 x-direction polarized array elements, and the positions of all array elements form the x-direction position vector vector is the x-direction polarized array element position indication vector, containing discontinuous integers, γ m1 is the m1-th element in the vector γ, m1 = 1, 2,..., M1, d represents the minimum interval between array elements, taking d ≤ λ / 2, λ is the signal wavelength, (·) T represents the transpose operation;

[0010] The y-direction polarized sub-array contains M2 y-direction polarized array elements, and the positions of all array elements form the y-direction position vector vector is the y-direction polarized array element position indication vector, containing discontinuous integers, η m2 is the m2-th element in the vector η, m2 = 1, 2,..., M2;

[0011] The two non-uniform sub-arrays together form a uniform linear array, the number of array elements M = M1 + M2, and the positions of its array elements form the vector (γ ∪ η)d, where the vector γ ∪ η contains continuous non-repeating integers, and ∪ represents the merging operation.

[0012] Step (2) Construct a partially polarized signal reception model and sample:

[0013] K narrowband uncorrelated signals from the direction of θ = [θ1, θ2,..., θ K T are incident on the non-uniform polarization array from the y-z plane; where θ k is the angle of the k-th incident signal from the positive semi-axis of the y-axis to each incident signal direction in the counterclockwise direction, k = 1, 2,..., K.

[0014] The output of the x-direction polarized sub-array at the t-th snapshot is represented by the following vector:

[0015] where, represents the steering vector of the x-direction polarized sub-array for the k-th signal; a x (θ k )'s m1-th element is s k,h (t) represents the horizontal polarization component of the k-th signal at the t-th snapshot, ε x (t) is the noise variance at the t-th snapshot as σ​2 A vector composed of zero-mean Gaussian white noise; the manifold matrix of the x-direction polarizer array A vector composed of the horizontal polarization components of each signal Denotes the complex number field;

[0016] The output of the y-direction polarizer array at the t-th snapshot is represented by the following vector:

[0017] Where, Denotes the steering vector of the y-direction polarizer array for the k-th signal; a y (θ k ) The m2-th element is s k,v (t) is the vertical polarization component of the k-th signal at the t-th snapshot; ε y (t) is a noise vector that is independently and identically distributed with ε x (t); the manifold matrix of the y-direction polarizer array A vector composed of the vertical polarization components of each signal

[0018] The k-th partially polarized signal s k (t)=[s k,h (t), s k,v (t)] T The coherence matrix of is defined as:

[0019] Where, Ε(·) represents taking the expectation, r k,hh , r k,vv respectively represent the powers of the k-th signal in the horizontal and vertical directions, and r k,hv represents the correlation coefficient between the two polarization components of the k-th signal. And are respectively the unpolarized power and the fully polarized power of the k-th signal. The polarization degree of the signal is expressed as ρ k ∈[0,1]. I2 represents the second-order identity matrix, (·) H represents taking the conjugate transpose, and (·) * represents taking the conjugate.

[0020] Rotation matrix α k represents the polarization direction angle of the k-th signal, -π / 2 < α k ≤π / 2;

[0021] The ellipticity vector w(β k ) = [cosβ k jsinβ k )T , β k represents the polarization ellipticity angle of the k-th signal, -π / 4 ≤ β k ≤ π / 4; then, at time t, all the outputs of the array are:

[0022] t = 1, 2, …, T, where T represents the number of snapshots; the noise included in all the outputs of the array at the t-th snapshot

[0023] Step (3) Calculate the sample covariance matrix of the array and its error statistical distribution:

[0024] The theoretical covariance matrix R corresponding to the array output = E[z(t)z(t) H , and the sample covariance matrix corresponding to the array output The error between and R is the model noise, which satisfies the following distribution:

[0025] where represents an asymptotically complex normal distribution with a mean of 0 and a covariance matrix of ∑, represents the Kronecker product, and vec(·) represents vectorizing the matrix column by column.

[0026] Step (4) Construct and solve an optimization problem for reconstructing the theoretical covariance matrix of the co-located uniform polarization array:

[0027]

[0028]

[0029]

[0030]

[0031] R x ′ x , R y ′ y ∈ Toeplitz; where ||·|| * represents the nuclear norm, ||·||2 represents the 2-norm, and τ is the regularization parameter; R′ represents the covariance matrix of the co-located uniform polarization array to be reconstructed, R x ′ x represents the covariance matrix of the x-direction polarization sub-array in the co-located uniform polarization array, and R y ′ y represents the covariance matrix of the y-direction polarization sub-array in the co-located uniform polarization array, and Rx ′ y represents the cross-covariance matrix between the x-direction polariton array and the y-direction polariton array in the co-located uniform polarization array; R x ′ y (γ, η) represents the sub-matrix formed by taking the corresponding rows and columns of matrix R x ′ y according to the element values in γ and η respectively; R x ′ x (γ, γ) represents the sub-matrix formed by taking the corresponding rows of matrix R x ′ x according to the element values in γ, and the corresponding columns of matrix R x ′ x finally; R y ′ y (η, η) represents the sub-matrix formed by taking the corresponding rows of matrix R y ′ y according to the element values in η, and the corresponding columns of matrix R y ′ y finally. R x ′ x , R y ′ y ∈ Toeplitz indicates that matrix R x ′ x R y ′ y is a Toeplitz matrix.

[0032] The optimization problem in the above formula is a convex optimization problem, which is solved by the interior point method or by using the mathematical toolbox CVX to obtain the estimated value of R′ σ 2 's estimated value R x ′ x 's estimated value and R y ′ y 's estimated value matrix

[0033] Step (5) estimates the signal arrival direction based on the reconstructed co-located uniform polarization array theoretical covariance matrix:

[0034] Sum the estimated values and to get Perform eigenvalue decomposition on it, and extract the signal subspace U formed by the eigenvectors corresponding to the K largest eigenvalues s ;

[0035] The mapping matrix is obtained by deleting Us The matrix obtained after the first row of U s is the matrix obtained by deleting the last row of U s ; denotes the pseudo-inverse of the matrix;

[0036] Performing eigenvalue decomposition on Ψ gives K eigenvalues ρ k , k = 1, 2, …, K, then the direction estimation of the signal is:

[0037] where, Arg(·) denotes the principal value of the argument of a complex number, and arccos[·] denotes the inverse cosine.

[0038] Step (6) Solve the signal coherence matrix and estimate the signal polarization parameters:

[0039] (6-1) Using the estimated direction of arrival to reconstruct the coherence matrix of each partial polarization signal

[0040] (6-1-1) Estimate the noise variance, using the following two denoising methods:

[0041] Method ① is to use the subspace method to perform eigenvalue decomposition on the reconstructed , then sort its eigenvalues to obtain its 2M - 2K smallest eigenvalues, and take the average as the noise variance of the reconstructed signal;

[0042] Method ② is obtained by solving the optimization problem in step (4);

[0043] (6-1-2) Remove the noise variance component:

[0044] The covariance matrix reconstructed after removing the noise component is the obtained noise variance;

[0045] (6-1-3) Reconstruct the coherence matrix of each partial polarization signal

[0046] First, calculate the transformation matrix is the steering vector of the reconstructed co-located uniform polarization array with respect to , the m-th element of m = 1, 2,..., M;

[0047] Then, calculate three intermediate parameter vectors respectively: where, (. / ) denotes element-wise division, i.e., dot division, then the formula for reconstructing the signal coherence matrix is:

[0048] (6-2) Process each estimated signal coherence matrix to reconstruct the k-th coherence matrix obtained.

[0049] For perform eigenvalue decomposition. The two eigenvalues obtained from the eigenvalue decomposition are b k,1 , b k,2 , and b k,1 > b k,2 , b k,2 The corresponding eigenvector ζ k = [ζ k,1 , ζ k,2 T Then the polarization degree estimation of the signal is: Polarization direction angle and polarization ellipticity angle are estimated as: Intermediate variable arctan[·] represents the arctangent operation.

[0050] Compared with the prior art, the present invention has the following beneficial effects: In the multi-parameter estimation method for partially polarized signals based on a non-collocated non-uniform polarization array proposed by the present invention, the array adopts a non-collocated manner, and the phase centers of each polarization unit do not overlap. On the one hand, it avoids the mutual coupling problem existing between the polarization units of the collocated array; on the other hand, each array element has only one RF channel, saving resources. The array adopts a non-uniform manner, removing the limitation on the array aperture and ensuring that there is no ambiguity in the direction-of-arrival estimation, better meeting the requirements of parameter estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is the overall flow block diagram of the method of the present invention;

[0052] Figure 2 is the schematic diagram of the structure of the non-collocated non-uniform polarization array in the present invention;

[0053] Figure 3 is the schematic diagram of the structure of the collocated uniform polarization array reconstructed in the present invention;

[0054] Figure 4 is the schematic diagram comparing the estimation accuracy of the method of the present invention with the Cramer-Rao bound at different signal-to-noise ratios;

[0055] Figure 5 is the schematic diagram comparing the estimation accuracy of the method of the present invention with the Cramer-Rao bound at different numbers of snapshots;

[0056] Figure 6 is the schematic diagram of the polarization degree estimation accuracy of the method of the present invention at different signal-to-noise ratios.​ Detailed implementation manners

[0057] The technical solutions and effects of the invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0058] As Figure 1 shown, the multi-polarization array receiving and direction finding method for partially polarized signals based on switches is specifically as follows:

[0059] Step 1: Arrange a non-coplanar non-uniform polarization array: This array is composed of two non-uniform sub-arrays. The polarizations of the two sub-arrays are orthogonal to each other and together form a uniform linear array. Each array element in the sub-array is composed of only one polarization unit, that is, each array element has only one output port.

[0060] The specific array arrangement method is as Figure 2 shown. In a three-dimensional rectangular coordinate system, two non-uniform sub-arrays are placed along the y-axis, namely the x-direction polarization sub-array and the y-direction polarization sub-array; where:

[0061] The x-direction polarization sub-array contains M1 x-direction polarization array elements, and the positions of all array elements form an x-direction position vector vector is the x-direction polarization array element position indication vector, which contains discontinuous integers, γ m1 is the m1-th element in the vector γ, m1 = 1, 2,..., M1, d represents the minimum interval between array elements, and d ≤ λ / 2 is taken, where λ is the signal wavelength, (·) T represents the transpose operation;

[0062] The y-direction polarization sub-array contains M2 y-direction polarization array elements, and the positions of all array elements form a y-direction position vector vector is the y-direction polarization array element position indication vector, which contains discontinuous integers, η m2 is the m2-th element in the vector η, m2 = 1, 2,..., M2;

[0063] The two non-uniform sub-arrays together form a uniform linear array, and the number of array elements M = M1 + M2. The positions of its array elements form a vector (γ ∪ η)d, where the vector γ ∪ η contains continuous non-repeating integers, and ∪ represents the merging operation.

[0064] Step 2: Construct a partially polarized signal reception model and sample: Assume that K narrowband uncorrelated signals from the direction of θ = [θ1, θ2,..., θ K T are incident on the non-uniform polarization array from the y-z plane; where θ k is the angle of the k-th incident signal from the positive half-axis of the y-axis to each incident signal direction in the counterclockwise direction, k = 1, 2,..., K. ​

[0065] The output of the x - direction polariton array at the t - th snapshot is represented by the following vector:

[0066] where, represents the steering vector of the x - direction polariton array for the k - th signal; a x (θ k )'s m1 - th element is s k,h (t) represents the horizontal polarization component of the k - th signal at the t - th snapshot, and ε x (t) is a vector composed of zero - mean Gaussian white noise with a noise variance of σ 2 at the t - th snapshot; the manifold matrix of the x - direction polariton array the vector composed of the horizontal polarization components of each signal represents the complex number field;

[0067] The output of the y - direction polariton array at the t - th snapshot is represented by the following vector:

[0068] where, represents the steering vector of the y - direction polariton array for the k - th signal; a y (θ k )'s m2 - th element is s k,v (t) is the vertical polarization component of the k - th signal at the t - th snapshot; ε y (t) is a noise vector that is independently and identically distributed with ε x (t); the manifold matrix of the y - direction polariton array the vector composed of the vertical polarization components of each signal

[0069] The coherence matrix of the k - th partially polarized signal s k (t)=[s k,h (t),s k,v (t)] T is defined as:

[0070] where, Ε(·) represents taking the expectation, r k,hh and r k,vv respectively represent the powers of the k - th signal in the horizontal and vertical directions, and r k,hv represents the correlation coefficient of the two polarization components of the k - th signal. and are respectively the unpolarized power and the fully polarized power of the k - th signal, and the polarization degree of the signal is expressed as ρ k∈[0,1]. I2 represents the second-order identity matrix, (·) H represents taking the conjugate transpose, (·) * represents taking the conjugate.

[0071] Rotation matrix α k represents the polarization pointing angle of the k-th signal, -π / 2 < α k ≤ π / 2;

[0072] Ellipticity vector w(β k ) = [cosβ k jsinβ k T , β k represents the polarization ellipticity angle of the k-th signal, -π / 4 ≤ β k ≤ π / 4; then, at time t, all outputs of the array are: t = 1, 2, …, T, T represents the number of snapshots; the noise included in all outputs of the array at the t-th snapshot

[0073] Step 3: Calculate the sample covariance matrix of the array and its error statistical distribution: The sample covariance matrix corresponding to the array output is denoted as The theoretical covariance matrix corresponding to the array output is denoted as: R = E[z(t)z(t) H . Due to the finite number of snapshots, there is an error between and R, which is called model noise and satisfies the following distribution:

[0074]

[0075] where represents an asymptotic complex normal distribution with a mean of 0 and a covariance matrix of ∑, represents the Kronecker product, and vec(·) represents vectorizing the matrix by columns.

[0076] Step 4: Construct and solve an optimization problem for reconstructing the theoretical covariance matrix of the co-located uniform polarization array:

[0077]

[0078]

[0079]

[0080]

[0081] R′ xx , R′​yy ∈ Toeplitz; where, ||·|| * denotes the nuclear norm, ||·||2 denotes the 2-norm, and τ is the regularization parameter; R′ represents the covariance matrix of the co-located uniform polarization array to be reconstructed, and the reconstructed co-located uniform polarization array is as Figure 3 shown. R′ xx represents the covariance matrix of the x-direction polarization subarray in the co-located uniform polarization array, and R′ yy represents the covariance matrix of the y-direction polarization subarray in the co-located uniform polarization array, and R′ xy represents the cross-covariance matrix between the x-direction polarization subarray and the y-direction polarization subarray in the co-located uniform polarization array; R′ xy (γ, η) represents the submatrix formed by taking the corresponding rows and columns of the matrix R′ according to the element values in γ and η respectively; R′ xy xx (γ, γ) represents the submatrix finally formed by taking the corresponding rows of the matrix R′ according to the element values in γ and the corresponding columns of the matrix R′ according to the element values in γ; R′ xx xx yy (η, η) represents the submatrix finally formed by taking the corresponding rows of the matrix R′ according to the element values in η and the corresponding columns of the matrix R′ according to the element values in η. R′ yy yy xx , R′ yy ∈ Toeplitz means that the matrix R′ xx R′ yy is a Toeplitz matrix. The optimization problem in the above formula is a convex optimization problem, which is solved by the interior point method or by using the mathematical toolbox CVX to obtain the estimated value of R′ σ 2 's estimated value R′ xx 's estimated value and R′ yy 's estimated value matrix In solving the above optimization problem, we minimize ||Σ -1 / 2 vec(ΔR)||, and this process is a whitening operation to remove the correlation between variables and make the solution result more accurate. A total of two types of noise are filtered out during the denoising process, namely the model noise ΔR and the array noise δ 2 I 2M .

[0082] Step 5: Estimate the signal arrival direction based on the reconstructed theoretical covariance matrix of the co-located uniform polarization array: The sum of the estimated values and ​​​​​​Perform eigen - decomposition to extract the signal subspace \(U\) composed of the eigen - vectors corresponding to the \(K\) largest eigenvalues s ;

[0083] Mapping matrix is the matrix obtained by deleting the first row of \(U\) s ; U s is the matrix obtained by deleting the last row of \(U\) s ; denotes the pseudo - inverse of the matrix; perform eigen - decomposition on \(\Psi\) to obtain \(K\) eigenvalues \(\rho\) k , \(k = 1,2,\cdots,K\), then the direction estimation of the signal is:

[0084] where \(Arg(\cdot)\) represents the principal value of the argument of a complex number, and \(arccos[\cdot]\) represents the inverse cosine.

[0085] Step 6: Solve the signal coherence matrix and estimate the signal polarization parameters:

[0086] (6 - 1) Use the estimated direction of arrival to reconstruct the coherence matrix of each part of the polarized signal

[0087] (6 - 1 - 1) Estimate the noise variance, using the following two denoising methods:

[0088] Method ① is to use the subspace method to perform eigen - decomposition on the reconstructed , then sort its eigenvalues to obtain its \(2M - 2K\) small eigenvalues, and take the average as the noise variance of the reconstructed signal;

[0089] Method ② is obtained by solving the optimization problem in step (4);

[0090] (6 - 1 - 2) Remove the noise variance component:

[0091] The covariance matrix reconstructed after removing the noise component is the solved noise variance;

[0092] (6 - 1 - 3) Reconstruct the coherence matrix of each part of the polarized signal

[0093] First, calculate the transformation matrix is the steering vector of the co - located uniform polarized array reconstructed for , the \(m\) - th element of \(m = 1,2,\cdots,M\);

[0094] Then, calculate three intermediate parameter vectors respectively: Among them, (. / ) represents element-wise division, i.e., dot division. Then, the signal coherence matrix reconstruction formula is:

[0095] (6-2) Process each estimated signal coherence matrix, and the k-th coherence matrix reconstructed is For Perform eigenvalue decomposition. The two eigenvalues of the eigenvalue decomposition are b k,1 , b k,2 , and b k,1 > b k,2 , b k,2 The corresponding eigenvector ζ k = [ζ k,1 , ζ k,2 T , then the polarization degree estimation of this signal is: Polarization direction angle and polarization ellipticity angle are estimated as: Intermediate variable arctan[·] represents the arctangent operation.

[0096] Next, the effectiveness of the present invention is verified by combining simulation examples. All statistical results are based on 500 Monte Carlo experiments.

[0097] Simulation example 1: To verify the estimation performance of the present invention, the following simulation experiments are carried out. Set the number of array elements M of the non-uniform polarization array to 8, M1 and M2 to 4, γ = [1, 2, 5, 7] T , η = [3, 4, 6, 8] T , the number of signal sources K to 2. The incident angles of the two signals are 85° and 95°, the polarization degrees are set to 0.9 and 0.9, the polarization direction angles α k = [0, 0], the polarization ellipticity angles β k = [-π / 6, π / 6], and the minimum spacing d between array elements is λ / 2. The signal-to-noise ratio is set to change from -8 dB to 20 dB, and the number of sampling snapshots is set to 200. Compare the root mean square error of the direction-of-arrival estimation of the method of the present invention with the estimation accuracy of the Cramer-Rao bound at different signal-to-noise ratios. The comparison results are as Figure 4 shown. It can be seen from the figure that as the signal-to-noise ratio increases, the curve of the method of the present invention gets closer and closer to the Cramer-Rao bound, and the estimation performance is stable. Subsequently, we fix the signal-to-noise ratio at 20 dB, change the number of snapshots from 50 to 500, and keep other parameters unchanged. Compare the root mean square error of the direction-of-arrival estimation of the method of the present invention with the estimation accuracy of the Cramer-Rao bound in the case of different numbers of snapshots. The comparison results are as Figure 5 ​As shown. It can be seen from the figure that the root mean square error of the method of the present invention at each snapshot number is very small and approaches the Cramer-Rao bound, having good estimation performance.

[0098] Simulation example 2: Verify the estimation accuracy of the polarization degree of the method of the present invention as the signal-to-noise ratio changes. The number of snapshots is fixed at 200, and the signal-to-noise ratio is set to change from -10 dB to 20 dB. Other simulation conditions are the same as those in the previous experiment. From Figure 6 it can be seen that the root mean square error of the polarization degree decreases as the signal-to-noise ratio increases, having high estimation accuracy. The following table shows the estimation table of the polarization parameters of the method of the present invention when the signal-to-noise ratio is 10 dB and the other simulation conditions are the same as those in the above experiment:

[0099]

[0100] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A multi-parameter estimation method for partially polarized signals based on a non-collocated non-uniform polarization array, characterized in that: Step (1) Arrange a non-collocated non-uniform polarization array: The non-collocated non-uniform polarization array is composed of two non-uniform sub-arrays. The polarizations of the two sub-arrays are orthogonal to each other and jointly form a uniform linear array. Each element in the sub-array is composed of only one polarization unit, that is, each element has only one output port. The specific arrangement method of the uniform linear array is as follows: In a three-dimensional rectangular coordinate system, two non-uniform sub-arrays are placed along the y-axis, namely the x-direction polarization sub-array and the y-direction polarization sub-array. Among them: The x-direction polarizer array includes M1 x-direction polarization array elements, and the positions of all array elements form an x-direction position vector vector is the position indication vector of the x-direction polarization array element, including discontinuous integers, γ m1 is the m1-th element in the vector γ, m1 = 1, 2, …, M1, d represents the minimum interval between array elements, taking d ≤ λ / 2, λ is the signal wavelength, (·) T represents the transpose operation; The y-direction polarizer array includes M2 y-direction polarization array elements, and the positions of all array elements form a y-direction position vector vector is the y-direction polarization array element position indication vector, including discontinuous integers, η m2 is the m2-th element in the vector η, where m2 = 1, 2, …, M2; The two non-uniform sub-arrays jointly form a uniform linear array, and the number of array elements M = M1 + M2. The positions of its elements form a vector (γ ∪ η)d, where the vector γ ∪ η contains consecutive non-repeating integers, and ∪ represents the merging operation. Step (2) Construct a partially polarized signal reception model and sample: K narrowband uncorrelated signals from the direction of θ = [θ1, θ2,..., θ K T are incident on the non-uniform polarization array from the y-z plane; where θ k is the angle of the k-th incident signal from the positive semi-axis of the y-axis to the incident direction in the counterclockwise direction, k = 1, 2,..., K;​ The output of the x-direction polarization sub-array at the t-th snapshot is represented by the following vector: Denote the steering vector of the x - direction polaron array for the k - th signal; a x (θ k ) The m1 - th element of is s k,h (t) represents the horizontal polarization component of the k - th signal at the t - th snapshot, ε x (t) is a vector composed of zero - mean Gaussian white noise with noise variance σ 2 at the t - th snapshot; the manifold matrix of the x - direction polaron array The vector composed of the horizontal polarization components of each signal Denote the complex number field; The output of the y-direction polarization sub-array at the t-th snapshot is represented by the following vector: Denote the steering vector of the y - direction polariton array for the k - th signal; a y (θ k )'s m2 - th element is s k,v (t) is the vertical polarization component of the k - th signal at the t - th snapshot; ε y (t) is a noise vector that is independently and identically distributed with ε x (t); the manifold matrix of the y - direction polariton array The vector formed by the vertical polarization components of each signal The k-th partially polarized signal s k (t) = [s k,h (t), s k,v (t)] T has a coherence matrix of: E(·) represents taking the expectation, and r k,hh , r k,vv respectively represent the power of the k-th signal in the horizontal and vertical directions, and r k,hv represents the correlation coefficient of the two polarization components of the k-th signal; and are respectively the unpolarized power and the fully polarized power of the k-th signal. The polarization degree of the signal is expressed as ρ k ∈[0,1]; I2 represents the second-order identity matrix, and (·) H represents taking the conjugate transpose, and (·) * represents taking the conjugate; Rotation matrix α k represents the polarization pointing angle of the k-th signal -π / 2＜α k ≤π / 2； Ellipticity vector w(β k ) = [cosβ k jsinβ k T , β k represents the polarization ellipticity angle of the k-th signal,​ -π / 4≤β k ≤π / 4； Then, at time t, all the outputs of the array are as follows: T represents the number of snapshots; the noise included in all the outputs of the array at the t-th snapshot Step (3) Calculate the array sample covariance matrix and its error statistical distribution: The theoretical covariance matrix R corresponding to the array output = E[z(t)z(t) H , the sample covariance matrix corresponding to the array output The error existing between and R is the model noise and satisfies the following distribution: Among them, represents an asymptotically complex normal distribution with a mean of 0 and a covariance matrix of ∑, represents the Kronecker product, and vec(·) represents vectorizing a matrix column by column; Step (4) Construct an optimization problem for reconstructing the theoretical covariance matrix of the collocated uniform polarization array and solve it: R′ xx , R′ yy ∈ Toeplitz; where, ||·|| * denotes the nuclear norm, ||·||2 denotes the 2-norm, and τ is the regularization parameter; R′ represents the covariance matrix of the co-located uniform polarization array to be reconstructed, R′ xx represents the covariance matrix of the x-direction polarization sub-array in the co-located uniform polarization array, R′ yy represents the covariance matrix of the y-direction polarization sub-array in the co-located uniform polarization array, R′ xy represents the cross-covariance matrix between the x-direction polarization sub-array and the y-direction polarization sub-array in the co-located uniform polarization array; R′ xy (γ, η) represents the sub-matrix formed by taking the rows and columns corresponding to the element values in γ and η respectively from the matrix R′ xy ; R′ xx (γ, γ) represents the sub-matrix finally formed by taking the rows corresponding to the element values in γ from the matrix R′ xx and taking the columns corresponding to the element values in γ from the matrix R′ xx ; R′ yy (η, η) represents the sub-matrix finally formed by taking the rows corresponding to the element values in η from the matrix R′ yy and taking the columns corresponding to the element values in η from the matrix R′ yy ; R′ xx , R′ yy ∈ Toeplitz means the matrix R′ xx R′ yy is a Toeplitz matrix; The estimated value of R′ is obtained by solving σ 2 The estimated value of R′ xx The estimated value of and the estimated value matrix of R′ yy The estimated value matrix of Step (5) Estimate the signal arrival direction based on the reconstructed theoretical covariance matrix of the collocated uniform polarization array: The estimated value and of the sum are subjected to eigen decomposition to extract the signal subspace U composed of the eigenvectors corresponding to the K largest eigenvalues s ; Mapping matrix is the matrix obtained by deleting the first row of U s . U s is the matrix obtained by deleting the last row of U s . denotes finding the pseudo-inverse of the matrix; Performing eigen - decomposition on Ψ to obtain K eigenvalues ρ k , where k = 1, 2, …, K, then the direction estimation of the signal is: Arg(·) represents finding the principal value of the argument of a complex number, and arccos[·] represents finding the inverse cosine; Step (6) Solve the signal coherence matrix and estimate the signal polarization parameters: (6-1) Using the estimated direction of arrival Reconstruct the coherence matrix of each part of the polarized signal (6-2) Process each estimated signal coherence matrix to reconstruct the k-th coherence matrix obtained Pair Perform eigenvalue decomposition. The two eigenvalues obtained from the eigenvalue decomposition are b k,1 , b k,2 , and b k,1 > b k,2 , b k,2 The corresponding eigenvector ζ k = [ζ k,1 , ζ k,2 T Then the polarization degree estimation of the signal is as follows: Polarization direction angle and polarization ellipticity angle are estimated as: Intermediate variable arctan[·] represents the calculation of the arctangent.​ 2. The multi-parameter estimation method for partially polarized signals based on a non-coplanar non-uniform polarization array according to claim 1, wherein Step (4) is solved using the interior point method or solved using the mathematical toolkit CVX to obtain an estimated value of R′ σ 2 estimated value of R′ xx estimated value of and the estimated value of R′ yy estimated value matrix 3. The multi-parameter estimation method for partially polarized signals based on a non-coplanar non-uniform polarization array according to claim 1, characterized in that (6-1) Specifically: (6-1-1) Estimate the noise variance, and adopt the following two denoising methods: Method ① uses the subspace method to perform eigenvalue decomposition on the reconstructed features, and then sorts its eigenvalues to obtain its 2M - 2K smallest eigenvalues. The average of these eigenvalues is the noise variance of the reconstructed signal. Method ② is obtained by solving the optimization problem in step (4); (6-1-2) Remove the noise variance component: The covariance matrix of the reconstructed output after removing the noise components is the noise variance obtained by solving; (6-1-3) Reconstruct the coherence matrix of the polarization signals of each part First, calculate the transformation matrix For the steering vector of the co-located uniform polarization array obtained by reconstruction with respect to the m-th element of ​ Then calculate three intermediate parameter vectors respectively: Among them, (. / ) represents element-wise division, that is, dot division. Then the signal coherence matrix reconstruction formula is:

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